At any instant of time $t$, the displacement of any particle is given by $2t-1$ (SI unit) under the influence of force of $5\,N$ . The value of instantaneous power is (in SI unit):
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : 10
To find the instantaneous power delivered by a force, we can use the formula:
$P=\vec{F}.\vec{v}$
where $P$ is the power, $\vec{F}$ is the force vector, and $\vec{v}$ is the velocity vector of the particle.
In this question, the force exerted is given as a constant $5\, N$. Since no direction is specified, and the displacement is given in a scalar form, we assume the force acts along the direction of displacement. Therefore, we can treat the vectors as scalars for simplicity.
The displacement of the particle is given by:
$x= 2t-1$
The velocity, $\vec{v}$ , is the derivative of displacement with respect to time. Deriving the displacement equation with respect to time $t$ gives:
$v=\frac{dx}{dt}=\frac{d}{dt}(2t-1)=2$
The instantaneous power can now be calculated as:
$P=F.v=5 × 2= 10\, Watts $
Thus, the instantaneous power delivered by the force at any time t is 10 Watts.
The correct answer is Option 1 : 10.